isomorphic

English

WOTD – 6 November 2013

Etymology

From iso- +‎ -morphic.

Pronunciation

• (UK) enPR: īsəmô'fĭk, IPA^(key): /ˌaɪ.səˈmɔː.fɪk/
• (US) enPR: īsōmôr'fĭk, IPA^(key): /ˌaɪ.soʊˈmɔɹ.fɪk/

• Audio (US):

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• Audio (General Australian):

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• Rhymes: -ɔː(ɹ)fɪk

Adjective

isomorphic (not comparable)

1. (mathematics) Related by an isomorphism; having a structure-preserving one-to-one correspondence.
   • 2003, Bernd Siegfried Walter Schröder, Ordered Sets: An Introduction, page 254:

     Let A, B be the ordered sets in Figure 10.3. Let C be the direct product of infinitely many copies of the two element chain 2. Then A^C is isomorphic to B^C, but A is not isomorphic to B.

2. (biology) Having a similar structure or function to something that is not related genetically or through evolution.
   • 1993, Marcus Jacobson, Foundations of Neuroscience, page 106:

     The fact that different structures can be shown to be functionally isomorphic implies that they are analogous, not homologous.

3. Having identical relevant structure; being structure-preserving while undergoing certain invertible transformations.
   • 1981, John Lyons, Language and Linguistics: An Introduction, page 60:

     For example, in so far as written and spoken English are isomorphic (i.e. have the same structure), they are the same language: there is nothing but their structure that they have in common.

Usage notes

• In mathematics, this adjective can be used in phrases like "A and B are isomorphic", "A is isomorphic to B", and, less commonly, "A is isomorphic with B".

Antonyms

• anisomorphic
• nonisomorphic

Coordinate terms

• anisomorphic
• heteromorphic
• homomorphic

Derived terms

• anisomorphic
• isomorphically

Related terms

• isomorph
• isomorphism
• isomorphous

Translations

(mathematics) related by an isomorphism

• Catalan: isomòrfic
• Chinese:

  Mandarin: 同構／同构 (zh) (tónggòu)

• Czech: izomorfní (cs)
• Dutch: isomorf (nl)
• Esperanto: ^{(please verify)} izomorfa
• Finnish: isomorfinen
• French: isomorphe (fr)
• German: isomorph (de)
• Hungarian: izomorf (hu)
• Irish: iseamorfach
• Japanese: 同型の (ja) (dōkei no)
• Latin: isomorpha f
• Lithuanian: izomorfinis
• Polish: izomorficzny
• Portuguese: isomorfo (pt), isomórfico (pt)
• Russian: изомо́рфный (ru) (izomórfnyj)
• Serbo-Croatian:

  Cyrillic: изоморфно

  Roman: izomorfno

• Spanish: isomorfo
• Swedish: isomorf (sv)

(biology) having a similar structure or function without genetic relation

• Catalan: isomòrfic
• Esperanto: ^{(please verify)} izomorfa
• Finnish: isomorfinen
• Irish: iseamorfach

having identical relevant structure

• Catalan: isomòrfic
• Esperanto: ^{(please verify)} izomorfa
• Finnish: isomorfinen
• Irish: iseamorfach
• Swedish: isomorf (sv)

Further reading

• isomorphic keyboard on Wikipedia.Wikipedia